Related papers: Parallel Transport over Path Spaces
We present a geometric framework for discrete classical field theories, where fields are modeled as "morphisms" defined on a discrete grid in the base space, and take values in a Lie groupoid. We describe the basic geometric setup and…
An analog of the classical Doppler effect is investigated in spaces (manifolds) whose tangent bundle is endowed with a transport along paths, which, in particular, can be parallel one. The obtained results are valid irrespectively to the…
The goal of these notes is to provide an introduction to rough partial differential equations. For this purpose, we will present the theory of rough paths to the extend as it is required. Applications to stochastic partial differential…
We propose a microscopic decision model for route choice based on discrete choice theory. The correlation of overlapping routes is included in the random portions of the utility explicitly. For computational efficiency, we restrict the…
A discrete model of traffic on a multilane road is considered. The traffic is presented as particles movement with a deterministic component and a stochastic one. Formulas for the traffic characteristics have been found. The model can…
We investigate the hitherto unexplored relation between the superparticle path integral and superfield theory. Requiring that the path integral has the global symmetries of the classical action and obeys the natural composition property of…
In this paper we introduce a notion of parallel transport for principal bundles with connections over differentiable stacks. We show that principal bundles with connections over stacks can be recovered from their parallel transport thereby…
The aim of this work is to lay the foundations of differential geometry and Lie theory over the general class of topological base fields and -rings for which a differential calculus has been developed in recent work (collaboration with H.…
In this paper we investigate the ability of some recently introduced discrete kinetic models of vehicular traffic to catch, in their large time behavior, typical features of theoretical fundamental diagrams. Specifically, we address the…
In the current book I suggest an off-road path to the subject of optimal transport. I tried to avoid prior knowledge of analysis, PDE theory and functional analysis, as much as possible. Thus I concentrate on discrete and semi-discrete…
A geometric interpretation of curvature and torsion of linear transports along paths is presented. A number of (Bianchi type) identities satisfied by these quantities are derived. The obtained results contain as special cases the…
Andreka and her colleagues have described various geometrically inspired first-order theories of special and general relativity, while Szekely's PhD dissertation focuses on an intermediate logic of accelerated observers. In this paper we…
An objective of the theory of combinatorial groupoids is to introduce concepts like "holonomy", "parallel transport", "bundles", "combinatorial curvature" etc. in the context of simplicial (polyhedral) complexes, posets, graphs, polytopes,…
Group based moving frames have a wide range of applications, from the classical equivalence problems in differential geometry to more modern applications such as computer vision. Here we describe what we call a discrete group based moving…
We define an abstract framework called {\it discrete finite differences embedding} which can be used to obtain discrete analogue of formal functional relations in the spirit of category theory. For ordinary differential equations we exhibit…
The paper starts with discussion of applications of cycle spaces to transportation cost. After a short survey of the known results on cycle spaces, we turn to the study of minimal projections onto cycle spaces in the corresponding…
We study the problem of distributed traffic control in the partitioned plane, where the movement of all entities (robots, vehicles, etc.) within each partition (cell) is coupled. Establishing liveness in such systems is challenging, but…
The problem at the heart of this tutorial consists in modeling the path choice behavior of network users. This problem has been extensively studied in transportation science, where it is known as the route choice problem. In this…
The quantum walk was originally proposed as a quantum mechanical analogue of the classical random walk, and has since become a powerful tool in quantum information science. In this paper, we show that discrete time quantum walks provide a…
We define functorial isomorphisms of parallel transport along etale paths for a class of vector bundles on a p-adic curve. All bundles of degree zero whose reduction is strongly semistable belong to this class. In particular, they give rise…